JP4722925B2 - Residual frequency offset determination method, communication system, message transmission method, transmitter, message processing method, and receiver - Google Patents

Description

  The present invention relates to a residual frequency offset determination method, a communication system, a message transmission method, a transmitter, a message processing method, and a receiver.

  SISO (single input signal output) / OFDM (orthogonal frequency division multiplexing) system, that is, using subcarrier modulation based on OFDM for data transmission with one transmit antenna and one receive antenna In the system, a preamble is transmitted before user data is transmitted for various reasons. First, a short preamble is transmitted for timing synchronization and frequency synchronization, particularly for frequency offset estimation.

  In actual data communication, frequency offset estimation is necessary because the frequency of the local oscillator of the receiver cannot be expected to be equal to the frequency of the signal carrier generated by the transmitter. This is due in part to circuit constraints, particularly when the receiver is moving relative to the transmitter. This is because during relative movement, the Doppler shift is necessarily incorporated into the carrier frequency.

  The frequency offset can cause inter-carrier interference (ICI). In multi-carrier systems, such as systems that employ orthogonal frequency division multiplexing (OFDM), residual frequency offsets result in significant performance degradation.

  After the short preamble, only a relatively small long preamble is transmitted in the SISO / OFDM system (two in the case of a system based on the IEEE 802.11a standard, see Non-Patent Document 1). Since only a single channel is constructed, a small long preamble is sufficient for channel estimation.

  However, in the case of a multiple input multiple output (MIMO) system in which a plurality of transmission antennas are used, a plurality of physical channels are used for transmission. Therefore, in order to extract all channel information, more long preambles are required. is necessary. Indeed, for MIMO systems, it can be shown that the number of long preambles should be greater than or equal to the number of transmit antennas.

  When the number of long preambles is increased in this way as compared with the SISO system, the transmission time of the long preamble (also referred to as a long preamble duration) becomes longer than that of the SISO system. This further increases the amount of phase rotation of the data code following the long preamble in the presence of a residual frequency offset that occurs unintentionally due to the finite number of short preambles for frequency offset estimation in an actual communication system. It becomes.

  Due to severe distortion, the first transmitted data code is usually not properly corrected, and error bits and error packets are generated.

  Non-Patent Document 2 describes an estimator (estimator) for frequency estimation.

  In the above, the following documents are cited.

"Part 11: wireless LAN medium access control (MAC) and physical layer (PHY) specifications: Hight-speed physical layer in the 5 GHz band." IEEE std 802.11a-1999: Supplement to IEEE 802.11-1999, Sept. 1996 S. Kay, "Statistically / Computationally efficient frequency estimation", ICASSP'98, pp. 2292-2294, vol. 4, 1998

  An object of the present invention is to provide an improved method for estimating a residual frequency offset in a communication system.

  The above-described problem is achieved by a residual frequency offset determination method, a communication system, a message transmission method, a transmitter, a message processing method, and a receiver having the characteristics according to the independent claims.

  A method for determining a residual frequency offset between a transmitter and a receiver during data transmission via a communication channel, wherein the message is transmitted from the transmitter to the receiver via the communication channel. Is provided. The message includes at least one short preamble, at least one long preamble, and user data, and the at least one long preamble includes residual frequency offset determination information. The residual frequency offset is determined based on the residual frequency offset determination information.

  Further, a method for transmitting a message by a transmitter, comprising at least one short preamble, at least one long preamble, and user data, wherein the at least one long preamble includes residual frequency offset determination information. A transmission method is provided for generating a message comprising the message and transmitting the message to a receiver via a communication channel. Based on the residual frequency offset determination information, the receiver can determine a residual frequency offset between the transmitter and the receiver when data is transmitted through the communication channel.

Further, a method of processing a message by a receiver, comprising at least one short preamble, at least one long preamble, and user data, wherein the at least one long preamble includes residual frequency offset determination information. A processing method is provided for receiving an included message from a transmitter via a communication channel. Based on the residual frequency offset determination information, a residual frequency offset between the transmitter and the receiver in data transmission via the communication system is determined.
A processing method characterized by the above.

  Furthermore, a communication system, a transmitter, and a receiver according to the method for determining the residual frequency offset, the message transmission method, and the message processing method are provided.

  As an example, a long preamble is used for residual offset estimation. In this way, as in the case of a MIMO (Multiple input multiple output) system, even when a large number of long preambles are transmitted, a relatively large number of long preambles are required for channel estimation, so there is no data loss. Residual frequency offset can be estimated and compensated.

  The present invention can be used, for example, in a communication system compliant with WLAN 11n, that is, a wireless local area network (LAN), but may be used in a wide area communication system such as a mobile phone communication system.

  Embodiments of the invention arise from the dependent claims. The embodiment of the present invention described in the content of the method for determining the residual frequency offset is also effective for a communication system, a message transmission method, a transmitter, a message processing method, and a receiver.

  In one embodiment, the at least one short preamble includes frequency offset determination information, and the frequency offset is determined based on the frequency offset determination information.

  The data may comprise further residual frequency offset determination information, and the residual frequency offset determination may be performed based on the additional residual frequency offset determination information.

  In one embodiment, the communication channel comprises at least one data subchannel and at least one pilot subchannel.

  The at least one long preamble may further include channel estimation information serving as a basis for performing channel estimation to determine transmission characteristics of the communication channel, and the residual frequency offset determination information may include the at least one pilot. The channel estimation information may be transmitted via the at least one data subchannel.

  This means that the pilot subchannel is used in the long preamble transmission period to transmit a special code (ie, pilot code), which allows the receiver to perform residual frequency offset estimation. It becomes possible.

  In one embodiment, the message is transmitted via multiple transmit antennas. The message may be received via multiple receive antennas.

  The message is transmitted according to OFDM, for example.

  In one embodiment, if the residual frequency offset is determined based on the residual frequency offset determination information, at least one signal received during transmission of the message based on the determined residual frequency offset Phase compensation is performed on the values.

  For example, at a certain moment in time based on the frequency offset determination information transmitted so far, the determination of the residual frequency offset may be performed, and all received signal values are subsequently determined based on the determined frequency offset. Correction (ie, phase compensation) is performed. If more residual frequency offset determination information is subsequently received over time, the residual frequency offset may be determined again to improve the current estimate of the residual frequency offset.

  In the embodiment described later, a special pilot embedded in both the long preamble and data will be described. A recursive estimation algorithm based on the linear prediction method of Non-Patent Document 2 is described, and a compensation formula that weakens the influence on both channel estimation and data is given.

  Specific examples of the present invention will be described below with reference to the drawings.

  FIG. 1 is a diagram illustrating a communication system 100 according to an embodiment of the present invention.

  The communication system 100 includes a transmitter 101 (only part of which is shown in FIG. 1) and a receiver 102.

  The transmitter 101 includes a plurality of transmission antennas 103. Each transmission antenna 103 is used for signal transmission. Data (user data, preamble, etc.) transmitted by the transmission antenna 103 in the form of a radio signal is supplied to the transmission antenna 103 by a corresponding IFFT (inverse fast Fourier transform) unit 104. The radio signal transmitted by the transmitter is received by the receiver 102 via the plurality of receiving antennas 105.

  The subcarrier modulation compliant with OFDM (Orthogonal Frequency Division Multiplexing) is used to transmit a signal value from the transmitting antenna 103 to the receiving antenna 105.

  Due to relative motion or hardware circuit defects, the local oscillator of the receiver 102 cannot be guaranteed to operate at the exact same frequency as the transmitter 101, and the disparity rotates the received signal at an angle that increases with time. Cause a frequency offset.

  Therefore, the short preamble is transmitted before the user data. This is shown in FIG.

  FIG. 2 is a diagram illustrating a transmission block 200 according to an embodiment of the present invention.

  The transmission block 200 is transmitted from left to right. That is, the leftmost element of the transmission block 200 is transmitted first.

  The transmission block 200 includes a plurality of short preambles 201 transmitted first. The short preamble 201 is used for frequency offset estimation by the frequency offset estimation (FOE) unit 106 of the receiver 102 after receiving the short preamble 201. The FOE unit 106 estimates the frequency offset represented by Ψ in FIG. The frequency offset compensation unit 107 receives the frequency offset estimated value ψ as an input, and further compensates the frequency offset for all the received signal values.

  After frequency offset compensation, the residual frequency offset is usually small, but still remains in the form of inter-carrier interference that destroys the orthogonality between the frequency subcarriers, and if this is not compensated for it will cause a total system failure. End up.

In the IEEE 802.11a standard, the frequency subchannels with indices [8, 22, 44, 58] (see 1 to 64 conventions) are single input single output (SISO) with 64 frequency subcarriers. Dedicated to pilot transmission in the system. It is assumed that the communication system 100 is a multiple input multiple output (MIMO) system including N _t transmit antennas 103 and N _R receive antennas 105. The frequency subchannel similar to the IEEE802.11a standard, that is, the frequency subchannel with the index [8, 22, 44, 58] is used for distributing pilot codes in this embodiment, as will be described later.

  The transmission block 200 includes a plurality of long preambles 202 transmitted after the short preamble.

The signal value of the long preamble 202 transmitted on the frequency subchannel of the index [8, 22, 44, 58] is given by Λ _{f, t, n} . Where Λ _{f, t, n} represents a signal value transmitted on the subchannel f via the transmission antenna t at time n. These signal values are also referred to as pilots embedded in the long preamble.

  Receiver 102 receives discrete signal values (in the frequency domain) at time n via receive antenna r and subchannel f.

Here, H _{f, r, t} is the channel gain of the subchannel f constructed between the transmitting antenna t and the receiving antenna r. ω represents the residual frequency offset at the receiver 102 (as described above, performed after performing frequency offset estimation and frequency offset compensation based on the short preamble 201). V _{f, r, n} is an AWGN sample.

The time index n is selected so that n = 1 corresponds to the beginning of the long preamble 201 and n = N _LP corresponds to the end of the long preamble 201.

Hereinafter, selection of Λ _{f, t, n} corresponding to f∈ [8, 22, 44, 58] will be described. Based on equation (1) These lambda _{f, t,} corresponding to _n L _{f, t, n,} after the treatment with the corresponding FFT section 108 is used by the residual frequency offset estimator 109, a residual frequency offset ω is Presumed.

As can be seen from equation (1), Λ _{f, t, n} is

If configured to be independent of t, such as

For all f and r in shaping noise samples at different times to the same variance by setting | Λ _{f, t} | = σ _x ² which implies a fixed power in each pilot code Would draw a complex sine function at n.

Because f∈ [8, 22, 44, 58] and r∈ [1, 2, ..., N _r ],

There are 4N _r independent complex sine functions with different amplitudes but equal frequency of 64Ω.

In order to match the pilot value in IEEE802.11a (see Non-Patent Document 1) as much as possible, in this embodiment, the assignment of Λ _{8, n} = −Λ _{22, n} = Λ _{44, n} = Λ _{58, n} = 1 is performed. Use.

In this embodiment, a long preamble structure without a cyclic prefix is used. In this case, the last 16 samples of the 64 samples of each long preamble code in the time domain need to be independent of n. This implies that for f∈ [8, 22, 44, 58], Λ _{f, n} = Λ _f . The above criteria can be summarized as follows.
C1) Independent of transmit antenna to generate independent complex sine function at receiver 102 C2) Assignment of subchannel pilot values consistent with IEEE 802.11a C3) To meet the requirement for long preamble structure without cyclic prefix Independence of time These criteria can be satisfied by formulating

For N _t = 6 and N _r = 3, this is shown in Table 1 for subchannel fε [8,44,58] and in Table 2 for subchannel f = 22.

式（２）とともに、位相補償の問題は、シングルトーンパラメータ推定の一つへと変わる。これは、信号処理分野では古典的であり、文献に既に多様な解決法がある。線形予測推定量（非特許文献２参照）は、計算の複雑さが妥当な所ではまずまず正確に作用し、また非特許文献２に導入されたカイ推定量と比較して、実施の点から見ると、特に魅力的である。単一サブチャネルf及び単一受信アンテナrに対して、式（２）に適用される場合には、推定量（推定器）の出力は、次式を示す。

Together with equation (2), the phase compensation problem turns into one of single tone parameter estimation. This is classic in the field of signal processing and there are already various solutions in the literature. The linear prediction estimator (see Non-Patent Document 2) works fairly accurately where the computational complexity is reasonable, and is compared to the Chi estimator introduced in Non-Patent Document 2 in terms of implementation. And is particularly attractive. When applied to equation (2) for a single subchannel f and a single receive antenna r, the output of the estimator (estimator) is

For N _t = 6 and N _r = 3, L _{f, r, n} received by the receiver 102 is shown in Tables 3 to 5 (where time increases toward the bottom of the table).

Λ_f,t,nは、意図的にt及びnから独立しているため（上述の通り）、表３から表５における各列は、異なる振幅ではあるが等しい周波数である複素正弦関数を形成する。受信したロングプリアンブルを用いて、即ち、L_f,r,nを用いて、残留周波数オフセット推定部１０９は、残留周波数オフセット推定値

Since Λ _{f, t, n} is intentionally independent of t and n (as described above), each column in Tables 3-5 forms a complex sine function with different amplitudes but equal frequencies. To do. Using the received long preamble, that is, using L _{f, r, n} , the residual frequency offset estimation unit 109 uses the residual frequency offset estimation value.

(Depends on the current time given by the time index n). This generation is performed according to the following equation.

This is an extension of equation (4). The time index n = 2 corresponds to the second long preamble among the plurality of long preambles 202. n = 3 refers to the third long preamble among the plurality of long preambles 202. same as below. Residual frequency offset estimate

Note that is dependent on time (see time index n). If more L _{f, r, n} becomes available at the receiver 102 (corresponding to increasing time index n), the residual frequency offset estimate will typically improve further. When all the long preambles 202 are transmitted, the residual FOE unit 109 determines the residual frequency offset estimated value.

Would have generated

  Finally, the transmission block 200 comprises a plurality of data codes 203 transmitted by the transmitter 101 after the long preamble 202.

The signal value of the data code 203 transmitted on the frequency subchannel of the index [8, 22, 44, 58] is given by Γ _{f, t, n} . Where Γ _{f, t, n} represents a signal value transmitted on the subchannel f via the transmission antenna t at time n. These codes are also referred to as pilots embedded in the data code.

The pilot embedded in the data code can be expanded according to the same principle as the pilot embedded in the long preamble. In contrast to equation (1), the received signal value D _{f, r, n} corresponding to Γ _{f, t, n} is given by:

However, as described above, f identifies a subchannel, t is a transmission antenna, r is a reception antenna, and n is a time index.

Different notation to distinguish from V _{f, r, n}

Was adopted as an AWGN (additive white gaussian noise) sample. Unlike the long preamble Λ _{f, t, n, which} can be manipulated so as not to require a cyclic prefix, the data signal value Γ _{f, t, n} is assumed to have no such degree of freedom. In the case of OFDM (Orthogonal Frequency Division Multiplexing) used in this embodiment, each OFDM code is set to a length of 80M-ray code due to the presence of a cyclic prefix.

  As a result, the frequency of the equation (6) becomes 80Ω instead of 64Ω in the equation (1), and the reference C3 is no longer applicable. Thus, the pilot is independent of t but is selected depending on f and n. Or it is chosen quantitatively.

However, K _n ∈ [1, −1] is a function of n according to a pseudo-random sequence for the SISO pilot specified in the IEEE 802.11a standard (see Non-Patent Document 1).

The definitions based on equation (7) are shown in Table 6 for subchannel fε [8,44,58] and in Table 7 for subchannel f = 22 for N _t = 6 and N _r = 3. .

データ符号に埋め込まれたパイロット、即ち、f∈[8, 22, 44, 58]のD_f,r,nは、ロングプリアンブルに埋め込まれたパイロットと同様に、残留周波数オフセット推定部１０９により用いられ、よって残留周波数オフセットが推定される。

The pilot embedded in the data code, that is, D _{f, r, n with} f∈ [8, 22, 44, 58] is used by the residual frequency offset estimation unit 109 in the same manner as the pilot embedded in the long preamble. Thus, the residual frequency offset is estimated.

The part corresponding to equation (4) in estimating each of the tone frequencies in the 4N _r subchannels is:

Equation (8) is intentionally reached based on Equation (7) and the property K _n ε [1, −1]. By extending to multiple subchannels and rewriting in recursive form, equation (8) becomes:

  Cumulative sum generated by residual FOE unit 109 based on the long preamble according to equation (5)

Is used as the first value of a _DATA to improve accuracy. The exponential factor in the first line of equation (9) was introduced to explain the frequency difference resulting from the absence of a cyclic prefix in the long preamble, as shown in equations (2) and (6). The

  In one embodiment, there may be two signal field codes, where n = 1 corresponds to the first signal field (SF) code, n = 2 corresponds to the second SF code, and n = 3 Corresponds to the third SF code. same as below.

For N _t = 6 and N _r = 3, D _{f, r, n} received by the receiver 102 is shown from Table 8 (where time increases towards the bottom of the table).

表８から表１０における各列は、単一の複素正弦関数とみなすことができる。

Each column in Tables 8-10 can be considered as a single complex sine function.

Hereinafter, the influence of the residual frequency offset in the time domain on the code in the frequency domain will be described. For ease of explanation, consider the case where there is no noise, but the same argument applies to other cases. Time sequence _{y n (n = 1,2, ...} , N) , the multiplied complex sine function e ^j a ^{(ωn + Φ).} However, ω << 1. When performing a discrete Fourier transform on this product, the frequency domain signal can be described in matrix form as follows:

y _f = FP y _t (10)
However,

F is a Fourier transform matrix.

  The effect of the sine function

If the diagonal matrix Q should be modeled in the frequency domain, the following equation is obtained.

The above approximation applies to any orthogonal transform with fixed power to each component, such as a Hadamard matrix, as well as to the matrix F , and is accurate at diagonal entries. Tables 11 and 12 show the time domain model and the frequency domain model in association with each other based on such approximation.

The N _LP long preambles share one single cyclic prefix in 16 samples, but the following data codes each have one cyclic prefix. As the model shows, the discrete signal of the receive antenna r in the long preamble and data code segment is given by:

Since the received signal value is phase rotated in the time domain and frequency domain, the channel identified based on the distorted long preamble will be affected by the residual frequency offset ω over a relatively long estimation interval in the MIMO system. Can deviate significantly from the channel. According to equation (13), the N _LP long preambles collected by subchannel f and receiving antenna r are related to channel gain H _{f, r, t} and transmission value Λ _{f, t, t} by the following equation.

  In matrix form, the following equation can be described.

A conventional LS channel estimate that does not take into account the residual frequency offset is given by:

This equation uses the characteristics of equation (12) and is Λ = constant × F (or any orthogonal transform in which each component has equal power, such as a Hadamard matrix, instead of a Fourier transform). Given that This is quite effective for an optimal long preamble structure. According to the equation (14), when the MIMO-OFDM system adopts a VBLAST (Vertical Bell-Lab Layered Space-Time) structure, for example, the data code received at the time n by the subchannel f and the antenna r is expressed by the equation (14). Using 16), the following equation is obtained.

This implies the following equation:

  Amplitude decay

Since ω decreases after frequency offset estimation and compensation based on the short preamble, it is invariant in time and can be ignored. On the other hand, the phase rotation term is an increasing function of time and therefore cannot be ignored. Therefore, the received signal value Y _{f, r, n} is replaced by the following equation by the residual frequency offset compensator 110 in order to give a phase compensation amount to the distortion of both the channel estimation value and the data code.

  The collected signal values are then supplied to a zero forcing interference suppression (ZFIS) unit 111 that also acts as a channel equalizer (and for data detection). The output of the ZFIS unit 111 is supplied to a decoder 112 that performs data decoding.

The above development is derived for the VBLAST configuration, but it is easily shown that the same compensation equation in equation (19) is also valid for GSTBC (Groupwise Space-Time Block Code) systems. In addition, when a long preamble having a cyclic prefix is captured, it is possible to immediately apply the same phase compensation and reach the following equation.
Long preamble:

Data code:

Phase compensation:

These equations provide similar performance using a pilot structure based on equations (3) and (7). This is because there is a difference only when using long pre-angles is not very efficient when communicating information.

In the above embodiment, channel estimation is not required for pilot subchannels. Instead, a _{LP, n} is calculated after each long preamble is received according to equation (5).

When all OFDM codes arrive, a _{DATA, n} is updated as specified in equation (9). Phase compensation for Y _{f, r, n} is performed, and for the next processing such as channel equalization, the equation (19)

Is acquired.

  Simulation results show that this method provides almost complete compensation. Obviously, the implementation is simple because it only requires some unavoidable non-linear behavior intentionally.

  For MIMO / OFDM systems, in each long training preamble, signal field, and OFDM code, in one embodiment, to make coherent detection robust against frequency offset and phase noise. , 8 subcarriers are used for pilot signals. These pilot signals shall be attached to subcarriers -48, -34, -20, -6, 6, 20, 34, and 48. The pilots in the long training preamble are not modulated over time, but the signal field and OFDM data code pilots will be BPSK modulated with a pseudo binary sequence to prevent the generation of spectral lines. The contribution of pilot subcarriers to each OFDM code is described below.

The pilot subcarrier contribution to the nth OFDM code is generated by the Fourier transform of the sequence P- _{58, 58} or P- _{53, 53} given below.

  First, the following sequence is defined.

And
P _{−53, 53} = {P _−26,26 , 0, P _−26,26 }
P _{−58, 58} = {P _−26,26 , 0,0,0,0,0,0,0,0,0,0,0, P _−26,26 }
The polarity of the pilot subcarrier is controlled by the sequence _Pn . P _n is a 127 element cyclic extension and is given by:

Each sequence element is used for one OFDM code. The first and second elements P ₀ and P ₁ are multiplied by the pilot subcarriers of the first and second SINGAL (signal) codes, respectively. Meanwhile, element following from P ₂ is used for DATA (data) code.

It is a figure which shows the communication system which concerns on the Example of this invention. It is a figure which shows the transmission block which concerns on the Example of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100 Communication system 101 Transmitter 102 Receiver 103 Transmission antenna 104 IFFT (Inverse Fast Fourier Transform) part 105 Reception antenna 106 Frequency offset estimation (FOE) part 107 Frequency offset compensation part 108 FFT part 109 Residual frequency offset estimation part 110 Residual frequency offset Compensator 111 Zero Forcing Interference Suppression (ZFIS) 112 Decoder

Claims (12)

A method for determining a residual frequency offset between a transmitter and a receiver during data transmission over a communication channel, comprising:
Sending a message from the transmitter to the receiver via the communication channel;
The message includes at least one short preamble, at least one long preamble, and user data.
The at least one long preamble comprises residual frequency offset determination information;
A determination method characterized by determining the residual frequency offset based on the residual frequency offset determination information by a recursive estimation algorithm based on a linear prediction method.   The determination method according to claim 1, wherein the at least one short preamble includes frequency offset determination information, and the frequency offset is determined based on the frequency offset determination information.   The determination according to claim 1 or 2, wherein the data comprises further residual frequency offset determination information, and the residual frequency offset determination is performed based on the further residual frequency offset determination information. Method.   The determination method according to any one of claims 1 to 3, wherein the communication channel includes at least one data subchannel and at least one pilot subchannel.   The at least one long preamble further includes channel estimation information serving as a basis for performing channel estimation to determine transmission characteristics of the communication channel, and the residual frequency offset determination information includes the at least one pilot. The determination method according to any one of claims 1 to 4, wherein the determination method is transmitted via a subchannel, and the channel estimation information is transmitted via the at least one data subchannel.   The determination method according to claim 1, wherein the message is transmitted via a plurality of transmission antennas.   The determination method according to claim 1, wherein the message is received via a plurality of reception antennas.   The determination method according to claim 1, wherein the message is transmitted according to OFDM.   If the residual frequency offset is determined based on the residual frequency offset determination information, phase compensation is performed on at least one signal value received when transmitting the message based on the determined residual frequency offset The determination method according to claim 1, wherein: is executed. A communication system comprising a transmitter and a receiver,
The transmitter is configured to transmit a message from the transmitter to the receiver via a communication channel, and the message includes at least one short preamble, at least one long preamble, and user data. The at least one long preamble comprises residual frequency offset determination information;
The receiver uses a recursive estimation algorithm based on a linear prediction method to determine a residual frequency between the transmitter and the receiver during data transmission via the communication channel based on the residual frequency offset determination information. A communication system configured to determine an offset. A method of sending a message by a transmitter,
At least one short preamble, at least one long preamble, and user data, wherein the at least one long preamble generates a message comprising residual frequency offset determination information;
Sending the message to the receiver via a communication channel;
Based on the residual frequency offset determination information by a recursive estimation algorithm based on a linear prediction method, the receiver is configured to perform a residual between the transmitter and the receiver during transmission of data over the communication channel. A transmission method characterized in that a frequency offset can be determined. At least one short preamble, at least one long preamble, and user data, wherein the at least one long preamble is configured to generate a message comprising residual frequency offset determination information And
A transmitter configured to transmit the message to a receiver via a communication channel;
With
Based on the residual frequency offset determination information by a recursive estimation algorithm based on a linear prediction method, the receiver can perform a residual between the transmitter and the receiver during transmission of data via the communication channel. A transmitter characterized in that a frequency offset can be determined.

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